Ampere's Law in Classical Electrodynamics

In summary, the conversation discusses the validity of Ampere's law for short conductors passing through a loop. It is mentioned that the law is only valid for long conductors and requires strong symmetries. The concept of displacement current is also brought up and it is explained that it is verified theoretically through Maxwell's equations. It is clarified that a current loop is needed and that the electric field intensity changes due to the drift of electrons along a curved path. The conversation ends with a request for confirmation on the correctness of the explanation.
  • #1
CHUKKY
28
0
I do not know but I do not know if Ampers law is valid for short conductors passing through a loop. I did integrate and my integral was different from the expected I*U. The law seems to be valid only when long conductors pass through a loop but not short ones. Can anyone explain what am missing?
 
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  • #2
Ampere's law requires very strong symmetries to use properly. It's always valid, but the integral is very hard if edge effects are present.
 
  • #3
but is their a way to show that no matter the dimension of the conductor passing through the loop the integral of the magnetic field along the loop is the enclosed current times the permeability constant.or was this law arrived by empirical and not theoretical means.
 
  • #4
Well, you need to modify Ampere's law a little bit to include the so-called "displacement current". It is "verified" theoretically because it is one of Maxwell's equations. But of course, all physical laws must be verified experimentally.
 
  • #5
but wld displacement current avail for short conductor?nd it was a steady current.
 
  • #6
You need a current loop. The only reason you can neglect the "loop" part for the long wire is that you can say the other parts of the wire are far away. If you have a short conductor, you need to close the circuit to have current.
 
  • #7
Awesome i just taught about that. kk And so what you saying is that due to the fact that electrons need to drift along the curved path, electric field intensity changes and Maxwell's law then avail right?if I am right reply me. And thank you very much for resolving this issue if my post is right. If my post aint right please correct.
 

1. What is Ampere's Law in Classical Electrodynamics?

Ampere's Law in Classical Electrodynamics is a fundamental law in electromagnetism that relates the magnetic field to the electric current produced by a set of moving charges. It states that the line integral of the magnetic field around a closed loop is equal to the permeability of free space times the electric current passing through the loop.

2. Who discovered Ampere's Law?

Ampere's Law was discovered by the French physicist Andre-Marie Ampere in the early 19th century. He conducted experiments with electric currents and observed the relationship between the magnetic field and the electric current flowing through a wire.

3. How is Ampere's Law used in practical applications?

Ampere's Law is used in many practical applications, such as in the design of electric motors and generators, as well as in the construction of electromagnets. It is also used in the study of magnetohydrodynamics, which is the interaction between magnetic fields and electrically conducting fluids.

4. What is the difference between Ampere's Law and Gauss's Law?

Ampere's Law and Gauss's Law are both fundamental laws in electromagnetism, but they apply to different aspects of the electric and magnetic fields. Ampere's Law relates the magnetic field to the electric current, while Gauss's Law relates the electric field to the electric charge. Ampere's Law also takes into account the direction of the current, while Gauss's Law does not consider the direction of the charge.

5. Can Ampere's Law be applied to non-uniform magnetic fields?

Yes, Ampere's Law can be applied to non-uniform magnetic fields as long as the integral is taken over a closed loop and the current is known at every point along the loop. In cases where the magnetic field is not uniform, the law can be used to calculate the magnetic field at a specific point along the loop.

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